Given:$\frac{3}{7}+x=\frac{17}{7}$To do: We have to solve the given equation.Solution:$\frac{3}{7}+x=\frac{17}{7}$   [Transposing $\frac {3}{7}$ to R.H.S]We get,$x=\frac{17}{7}-\frac{3}{7}$$x=\frac{14}{7}$. $x=2$.The value of $x$ is $2$.

Given:\( 6=z+2 \).To do: We have to solve the given equation.Solution:$6=z+2$   [Transposing $2$ to L.H.S]We get,$6-2=z$$4=z$This implies$z=4$.The value of $z$ is $4$.

Given:\( y+3=10 \).To do: We have to solve the given equation.Solution:$y+3=10$   [Transposing $3$ to R.H.S]We get,$y=10-3$$y=7$.The value of $y$ is $7$.

Given:\( x-2=7 \).To do: We have to solve the given equation.Solution:$x-2=7$   [Transposing $-2$ to R.H.S]We get,$x=7+2$$x=9$.The value of $x$ is $9$.

Given:\( \frac{7 y+4}{y+2}=\frac{-4}{3} \)To do: We have to solve the given equation.Solution:$\frac{7 y+4}{y+2}=\frac{-4}{3}$$\Rightarrow 3(7y+4)=(-4) \times(y+2)$                [On cross multiplication]$\Rightarrow 21y+12=-4y-8$$\Rightarrow 21y+4y=-8-12$$\Rightarrow 25y=-20$$\Rightarrow y=\frac{-20}{25}$$\Rightarrow y=\frac{-4}{5}$The value of $y$ is $\frac{-4}{5}$. 

Given:\( \frac{3 y+4}{2-6 y}=\frac{-2}{5} \)To do: We have to solve the given equation.Solution:$\frac{3 y+4}{2-6 y}=\frac{-2}{5}$$\Rightarrow 5(3y+4)=(-2) \times(2-6y)$                [On cross multiplication]$\Rightarrow 15y+20=-4+12y$$\Rightarrow 15y-12y=-4-20$$\Rightarrow 3y=-24$$\Rightarrow y=\frac{-24}{3}$$\Rightarrow y=-8$The value of $y$ is $-8$. 

Given:\( \frac{z}{z+15}=\frac{4}{9} \)To do: We have to solve the given equation.Solution:$\frac{z}{z+15}=\frac{4}{9}$$\Rightarrow 9(z)=4 \times(z+15)$                [On cross multiplication]$\Rightarrow 9z=4z+60$$\Rightarrow 9z-4z=60$$\Rightarrow 5z=60$$\Rightarrow z=\frac{60}{5}$$\Rightarrow z=12$The value of $z$ is $12$. 

Given:\( \frac{9 x}{7-6 x}=15 \)To do: We have to solve the given equation.Solution:$ \frac{9 x}{7-6 x}=15$$\Rightarrow 9x=15 \times(7-6x)$                [On cross multiplication]$\Rightarrow 9x=105-90x$$\Rightarrow 9x+90x=105$$\Rightarrow 99x=105$$\Rightarrow x=\frac{105}{99}$$\Rightarrow x=\frac{35}{33}$The value of $x$ is $\frac{35}{33}$. 

Given:$0.25(4 f-3)=0.05(10 f-9)$.To do:We have to solve the given linear equation.Solution: $0.25(4 f-3)=0.05(10 f-9)$This implies,$0.25(4 f)-0.25(3)=0.05(10 f)-0.05(9)$$f-0.75=0.5f-0.45$$f-0.5f=0.75-0.45$$0.5f=0.30$$f =\frac{0.3}{0.5}$$f = \frac{3}{5}$$f=0.6$The value of $f$ is $0.6$. 

Given:$3(5 z-7)-2(9 z-11)=4(8 z-13)-17$.To do:We have to solve the given linear equation.Solution: $3(5 z-7)-2(9 z-11)=4(8 z-13)-17$This implies,$3(5z)-3(7)-2(9z)-2(-11)=4(8z)-4(13)-17$$15z-21-18z+22=32z-52-17$$-3z+1=32z-69$$32z+3z=69+1$$35z=70$$z =\frac{70}{35}$$z = 2$The value of $z$ is $2$.